Sparse sampled-data control of a family of high-order nonlinear systems with large delays in state and input

Abstract

This article studies the problem of sampled-data control for a family of high-order nonlinear systems with large delays in state and input. Under appropriate conditions, delay-free sampled-data state feedback controllers are designed based on the tool of adding a power integrator and the emulation method. Using the Lyapunov–Krasovskii functional theorem, combined with the robustness analysis, we prove that the nonsmooth sampled-data controllers thus constructed are capable of rendering the time-delay hybrid closed-loop system globally asymptotically stable, even under sparse sampling. The family of time-delay nonlinear systems under consideration contains uncontrollable linearization and requires nonsmooth rather than smooth feedback, and thus making the design of memoryless sampled-data controllers more subtle. Examples and simulations are given to validate the effectiveness of the proposed sampled-data controllers, with the emphasis on sparse sampling.